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Showing posts with label Algebra. Show all posts
Showing posts with label Algebra. Show all posts

Friday, April 22, 2011

That's WYCDWT - Speeding Tickets

"For each ticket, Mr. Foreman digitally superimposed the two photos - taken 0.363 seconds apart from a stationary point, according to an Optotraffic time stamp - creating a single photo with two images of the vehicle. Using the vehicle’s length as a frame of reference, Mr. Foreman then measured its distance traveled in the elapsed time, allowing him to calculate the vehicle’s speed. In every case, he said, the vehicle was not traveling fast enough to get a ticket."

Judges agreed.  Booyah.

Thursday, April 7, 2011

9 & 33 ... Thursday Tidbits

Problem 9
Difficulty: Not difficult at all.

Problem 33

Difficulty: Just algebra. If all kids took and passed algebra II, this problem would be easy for everyone..

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 09 and answer 33.

Wednesday, April 6, 2011

Let's make Algebra II mandatory - that'll learn them.

From Mother Jones and The Washington Post:  ed reform has gone to this:
Of all of the classes offered in high school, Algebra II is the leading predictor of college and work success, according to research that has launched a growing national movement to require it of graduates.
In recent years, 20 states and the District have moved to raise graduation requirements to include Algebra II, and its complexities are being demanded of more and more students.
....One of the key studies supporting the Algebra II focus was conducted by Anthony Carnevale and Alice Desrochers, then both at the Educational Testing Service. They used a data set that followed a group of students from 1988 to 2000, from eighth grade to a time when most were working. The study showed that of those who held top-tier jobs, 84 percent had taken Algebra II or a higher class as their last high school math course. Only 50 percent of employees in the bottom tier had taken Algebra II.
....But not everyone is convinced that Algebra II is the answer. Among the skeptics is Carnevale, one of the researchers who reported the link between Algebra II and good jobs. He warns against thinking of Algebra II as a cause of students getting good jobs merely because it is correlated with success. “The causal relationship is very, very weak,” he said. “Most people don’t use Algebra II in college, let alone in real life. The state governments need to be careful with this.”
Holy crap!  It's so damned simple!

Calculus students do really well in jobs that require mathematics.  Let's require every student to take calculus and we'll have a nation of math geniuses.

Algebra II! As a minimum requirement to hold a high school diploma! We're literally saying that if you can't factor polynomials, manipulate complex numbers, do matrix arithmetic, and understand basic trig, then you can't get a high school diploma? Really?
The push comes from Achieve, a group of idiots would really, really need to take statistics again.

Let's think here ... smart kids take algebra II ... smart kids are motivated ... smart kids are likely to maintain their motivation and work their way up the corporate ladder ... smart kids are likely to take art ... smart kids are likely to do well in literature ...  smart kids are likely to finish college ... smart kids do well in science ... smart kids work hard ... smart kids focus ... smart kids are likely to be smart ... smart kids eat healthy foods ... smart kids play a lot of video games ... smart kids read a lot ... smart kids play soccer ... smart kids volunteer their time ... smart kids eat crappy, greasy foods ... smart kids are likely to be athletic ... we could go on.

Why is anyone making the link only between algebra and success?

Why are we so stupid?

Wednesday: 8 and 34

Problem 8

Difficulty: Functions aren't my favorite, but this one held my interest.

Problem 34
Difficulty: Middling. Fascinating application of algebraic theory.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 08 and answer 34.

Tuesday, March 29, 2011

Tuesday Child is full of grace ... 20, 21, and 22.

Problem 20

Difficulty: Easy, but fun. A new way to look at averages and the effect of an addition on the average, depending on n.

Problem 21

Difficulty: Linear programming.Any bets this will somehow work out to an integer?

Problem 22


Difficulty: Easy. Once you've got the details right.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 20, answer 21 and answer 21.

Sunday, March 27, 2011

Delicious pair o'Problems: 18 and 24

Problem 2*3²

Difficulty: easy-ish. A little trigonometric - algebraic manipulation and "Surprise!"

Problem 2³*3

Difficulty: Easy. At least once in every test, in some form or another, the creators work the year into a problem.  This test was for 2007.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 18 and answer 24.

Saturday, March 26, 2011

Happy Saturday. Here's your daily double: 17 and 25.

Day Seventeen


Difficulty: easy-schmeasy, if you subtract. More complicated if you try to add.

Problem 25 = 5².
(I wonder how often you can switch the digits and still write an equivalent expression.)



Difficulty: Medium. More damned logarithms, but there's a neat little prime factorization going on, too.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 17 and answer 25.

Friday, March 25, 2011

Gruesome Twosome: 16 and 26

Sweet Sixteen

Difficulty: easy-ish. Another SAT-type reasoning question. Fun to watch the students work out the ramifications.

Problem 26

Difficulty: Medium. Is it wrong of me to get really annoyed at this question?  It's not terribly difficult, but it is so ... artificial.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 16 and answer 26.

Tuesday, March 22, 2011

Daily Think. Problems 13 and 29

Day Thirteen
Difficulty: easy-ish. Mostly, it's an interpretation question.

I love this next problem. So very cool.
Problem 29
i.e., find the shaded area.
Difficulty: Medium.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 13 and answer 29.

Sunday, March 20, 2011

Daily Two 11 and 31

First, an easy one.
And then something more complicated, though personally, I'm not a fan of probability questions.


Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 11 and answer 31.

Saturday, March 19, 2011

Daily two puzzles for contemplation. 10 and 32

Day Ten
Difficulty: easy-ish.

Problem 32:
Difficulty: Tricky. It seems easy, but then tries to kneecap you.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 10 and answer 32.

Friday, March 18, 2011

Daily Two. 9 and 33

Day Nine.
Difficulty: easy-ish.

Number 33: 

Difficulty: Hard.
(or as the kids said, OMFG)
It's actually more complicated than hard.

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 9 and answer 33.

Tuesday, March 15, 2011

Daily Pair of Problem Puzzles. 6 and 36

Day Six will make you think a bit.

Difficulty: easy - ish.

Difficulty: Hard (last page)

Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest

answer 6 and answer 36.

Friday, March 11, 2011

Daily Puzzle Pairing. 41

Since there are so many truly able mathematicians among my readers, I've decided to give them something to keep busy with! This set will start at the hardest and work backwards.

Difficulty: hard.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
Answer is here.

Thursday, October 28, 2010

PsuedoContext



Dan Meyer gives an example from "The Real World":
Santa Cruz Sentinel, today:
The City Council will consider a proposal today to establish a citywide pay-by-cell phone system that would allow motorists to start, finish and extend time for meters or fee-based parking spots. [..] Consumers would pay a fee of 35 cents per transaction, or 25 cents for frequent users if they are willing also to pay a monthly access fee of $1.75.

"Is pseudocontext a failure of imagination or is it a symptom of laziness? Because this sort of thing just isn't hard to find."
I think it's pretty lame of him to toss out this false dichotomy like that. (My browser settings and his comment system don't seem to be on speaking terms, so I'll mention this here.)  And I notice that he's been teaching for how long and only now noticed this gem? (I know that's unfair, but so is the original question.  I withdraw my snarky comment.)

No, the real problem here is one of timing, of not having this pop up in your newspaper on the day you need it, at the time you're doing the lesson planning. It's got little to do with a lack of imagination.  In fact, a lack of imagination is probably the best trait for someone doing lesson plans.  Teaching takes imagination -- why waste this limited resource on something as foolish as lesson plans?  What God in whichever Heaven you stare at when you can't see a ceiling decreed that you must know what the kids will be doing during the 13th minute of your class period? What if you needed to repeat something or -- swoon -- got off on a really good tangent?

Besides, not everyone spends every waking moment solely focused on teaching and mathematics. Sometimes, I just read.

It does take a certain frame of mind to watch for these things ... an old teacher friend of mine used to clip articles ... this is similar.  I never could get the hang of it with newspaper, but I do find it easier on the Internet. Now that I have been using the thumbdrive method of file transport, I have amassed a large library of these types of things, neatly sorted into the classes and folders so I can find them later when I get around to it. (Yeah, right)

Having said that, this "Real-World" problem is no more or less engaging to students than the cellphone plan that charges by the month or by the 100 minute-block or the psuedocontextual dreck in the book.

[So I had a five-minute bit of Photoshop fun at Dan's expense. Don't think nothing of it.]

On a scale of 1 to 10, these are funny.

So, there's this magic dust called "Math Teacher Magic Scale Factor" ... it makes things really big. Sometimes too big.


Wednesday, September 29, 2010

Skating Puzzle

It is recorded that in a mile race between two graceful skaters the rivals started from opposite points to skate to the other's place of beginning. With the advantage of a strong wind Jennie performed the feat two and a half times as quick as Maude, and beat her by six minutes. The problem, which has created no end of discussion, is to tell the time of each in skating the mile.

Sunday, June 13, 2010

How Old is Mary?


"You see," remarked GrandPa, "the combined ages of Mary and Ann are 44 years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when when Ann is three times as old as Mary was when Mary was three times as old as Ann.
How old is Mary?

~ Sam Loyd, Cyclopedia of Puzzles, 1914

Tuesday, June 8, 2010

Clock Puzzle

The picture of a clock dial illustrated the important point of evidence in a detective story where a stray bullet from the assassin's pistol struck the face of the clock.

It struck the exact center, driving the post through the works and stopping the clock. The two hands became united, as it were, in one line, pointing in opposite directions, although not in the direction shown, for it is evident that the hands could not point at three and nine at the same time.

Can you tell what time of day it must have been, thereby proving an alibi for the hero who wishes to show he was eating a plate of pig's knuckles in Hoboken at the time the pistol was fired in Sir Reginald's flat in Harlem?

- Sam Loyd, Cyclopedia of Puzzles, 1914


answer in this backdated post.

Wednesday, June 2, 2010

Letter to the Editor - WCYDWT?

Found this. What Can You do with It?
It costs more to use less
An Albany (NY) Times Union Letter to the Editor

It's bad enough that the town of Colonie, in tandem with the Latham Water District, has raised the cost per 1,000 gallons of water usage a number of times over the past few years. Now, the minimum charge has been raised so that anyone trying to conserve water will pay more than the base rate.

In the last six months, my water usage decreased by 5,000 gallons, but instead of paying for the water at the rate of $2.65 per 1,000 gallons, I've been assessed a minimum charge of $3.25 per 1,000 gallons because I failed to use as much water as the town thought I should use. Unless your usage is more than 20,000 gallons in a six-month period, you will be zapped with a higher rate.

Why would I want to be careful about water usage when it will cost me more if I use less?

This administration apparently is taking a page out of the book of the state Legislature by trying to make up its deficit on the backs of the people it will hurt the most, the seniors. I believe the seniors are most likely the group who will use the least amount of water, yet pay more for it. Water conservation helps everyone and it should not be used as a tool for the town of Colonie to make money.

Robert Leffingwell
Colonie